Implementation of Lattices System in Homomorphic Encryption

Nowadays, amount of transmitted information grows exponential. If in the system is needed to change already encrypted information this information need to be decrypted, changed, and after it, it need to be encrypted again, it takes a lot of time. One of these systems is cloud storage. For solving problem of security of the cloud storage can be used Homomorphic Encryption (HE). This allows users to perform mathematical operations on plaintext encrypted data, performing homomorphic operations on ciphertext without decryption. This idea gives a great benefit in case of implementing it in cloud computing.Homomorphic Encryption is divided on Fully Homomorphic Encryption (FHE) and Partly Homomorphic Encryption (PHE). Firstly, FHE was presented in 2009, since that time many researches worked on the idea of creating FHE systems.This work demonstrates the idea of implementing ideal lattices for the construct homomorphic operations on ciphertexts.